Ising core-shell model was proposed to reconstruct superparamagnetism hysteresis in nano-goethite (α-FeOOH). Core and shell set as antiferromagnetic and paramagnetic state respectively. Core and shell radius varies until the theoretical hysteresis fit with experiment hysteresis. At low temperature, the hysteresis reconstructed nicely with 55% antiferromagnetic core contribution and 45% paramagnetic shell contribution. At high temperature, the core-shell model show unrealistic result compared to the pure paramagnetic state.
Effective operators within theab initiono-core shell model